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Properties

Label 3234.2.bw
Level $3234$
Weight $2$
Character orbit 3234.bw
Rep. character $\chi_{3234}(89,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2256$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3234.bw (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3234, [\chi])\).

Total New Old
Modular forms 8160 2256 5904
Cusp forms 7968 2256 5712
Eisenstein series 192 0 192

Trace form

\( 2256 q - 188 q^{4} - 28 q^{6} - 16 q^{7} - 32 q^{9} + O(q^{10}) \) \( 2256 q - 188 q^{4} - 28 q^{6} - 16 q^{7} - 32 q^{9} + 24 q^{15} + 188 q^{16} + 24 q^{19} - 16 q^{21} + 12 q^{24} + 196 q^{25} - 8 q^{28} - 8 q^{30} - 24 q^{31} + 20 q^{36} + 68 q^{37} + 12 q^{39} + 48 q^{42} - 16 q^{43} - 48 q^{45} + 312 q^{46} + 40 q^{49} + 12 q^{51} - 32 q^{52} + 36 q^{54} + 60 q^{57} + 52 q^{58} + 12 q^{60} - 112 q^{61} + 56 q^{63} + 376 q^{64} + 8 q^{67} - 32 q^{70} - 48 q^{73} - 132 q^{75} + 32 q^{81} - 24 q^{82} - 80 q^{84} - 128 q^{85} + 36 q^{87} - 84 q^{90} + 16 q^{91} + 536 q^{93} + 48 q^{94} + 12 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3234, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3234, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)